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If veca=i-2j+3k,vecb=2i+3j-4k and vecc...

If `veca=i-2j+3k`,`vecb=2i+3j-4k` and `vecc=i-3j+5k`,then check whether `veca`,`vecb`,`vecc` are coplanar.

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If veca=5i-j-3k and vecb=i+3j+5k ,then show that the vectors veca+vecb , veca-vecb are perpendicular.

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Let veca=2i-j+2k and vecb=6i+2j+3k Find the angle between veca and vecb .

Show that the points A, B and C with position vectors veca=3i-4j-4k,vecb=2i-j+k and vecc=i-3j-5k respectively form the vertices of a right angled triangle.

Show that if veca+vecb,vecb+vecc,vecc+veca are coplanar then veca,vecb,vecc are also coplanar.

If veca, vecb , vecc are the three vectors mutually perpendicular to each other and |veca| =1 , |vecb| = 3 and |vecc| = 5, then [veca -2 vecb, vecb - 3 vecc , vecc - 4 veca] is equal to a)0 b)-24 c)3600 d)-215

Let veca=2i-j+2k and vecb=6i+2j+3k .Find a unit vector in the direction of veca+vecb .

If veca=i-j+k and vecb=2i-2j-k . What is the projection of veca on vecb ?

If veca,vecb,vecc are coplanar,prove that veca+vecb,vecb+vecc,vecc+veca are coplanar.

MAXIMUM PUBLICATION-MODEL QUESTION-EXAMPLE
  1. If the vectors vec(PQ)=-3i+4j+4k and vec(PR)=-5i+2j+4k are the sides o...

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  2. If veca=5i-j-3k and vecb=i+3j+5k,then show that the vectors veca+vecb,...

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  3. If veca=i-2j+3k,vecb=2i+3j-4k and vecc=i-3j+5k,then check whether ve...

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  4. Find the Cartesian equation of the line passing through origin and (5,...

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  5. The point P(x,y,z) lies in the first octant and its distance from the ...

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  6. Solve graphically. Maximise Z=5x+3y Subject to the constraints 3...

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  7. A=[[3,3,-1],[-2,-2,1],[-4,-5,2]] Find A^T

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  8. Express the following matrices as the sum of a Symmetric and a Skew Sy...

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  9. If A^T=[[cosx,sinx],[-sinx,cosx]],Verify that A^TA=I

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  10. Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

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  11. Consider the following system of equations 2x-3y+5z=11, 3x+2y-4z=-5,x...

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  12. Consider the following system of equations 2x-3y+5z=11,3x+2y-4z=-5...

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  13. Find dy/dx of the following x^2+xy+y=100

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  14. Find dy/dx of the following y^x=2^x

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  15. Find dy/dx of the following x=costheta,y=sintheta at theta=pi/4

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  16. Evaluate the integrals intx/((x+1)(x+2))dx

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  17. Evaluate the following int0^1 xe^(x^2)dx

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  18. Evaluate the following int-5^5 abs[x+2]dx

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  19. Consider the parabolas y^2=4x,x^2=4y Draw a rough figure for the abov...

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  20. Consider the parabolas y^2=4x,x^2=4y Find the point of intersection ...

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